Important Formulas
Problems on Time and Work
Q11. 10 men can finish the construction of a wall in 12 days. How many men are added to finish the work in half a day ?
(a) 120
(b) 220
(c) 230
(d) 240
Answer: (c) 230
Let the total number of men be x
No. of men 10 x
No. of day 12 1/2
Now 10 X 12 = x X (1/2) [proportion is inverse, More man less time taken]
=> x = (10 X 12)/(1/2) = 10 X 12 X 2 = 240
∴ Number of men to be added = (240 - 10) = 230
Q12. 20 men complete one third of a piece of work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days ?
(a) 12
(b) 15
(c) 22
(d) 25
Answer: (a) 12
Work done = 1/3
Remaining work = (1 - 1/3) =2/3
Let the required number of men be x
| 1 | X 25 X (20+x) = | 2 | X 20 X 20 |
| 3 | 3 |
=> 20 + x = 800/25 = 32
=> x = 32 - 20 = 12
Q13. If 36 men can do a piece of work in 25 days, in how many days will 12 men do it ?
(a) 35
(b) 56
(c) 75
(d) 80
Answer: (c) 75
Let the required number of days be x
Now, 36 X 25 = 12 X x
⇒ x = (36 X 25)/12 = 75
Q14. The A Minar casts a shadow of 180m long at the same time when the B Minar casts a shadow of 120m long on the ground. If the height of the B Minar is 80m, what is the height of the A minar ?
(a) 105m
(b) 115m
(c) 120m
(d) 135m
Answer: (c) 120m
Let the required height of the A Minar be x m
A/Q x X 120 = 180 X 180
⇒ x = (180X180)/120 = 120m
Q15. 6 men can finish a piece of work in 30 days. If 3 men more join with them then the work will be completed in
(a) 18
(b) 20
(c) 22
(d) 24
Answer: (b) 20
Let the required time be x days
For 6 No. of Man = 30 No. of days
For 9 (6+3) No. of Man = x No. of days
A/Q 6 X 30 = 9 X x
⇒ x = (6X30)/9 = 20
Q16. 10 women can complete a work in 6 days and 10 children take 12 days to complete the work. How many days will 6 women and 4 children together take to complete the work ?
(a) 7½ days
(b) 8½ days
(c) 9½ days
(d) 10½ days
Answer: (a) 7½ days
10 women's 1 day's work = 1/6
1 women's 1 day's work = 1/60
6 women's 1 day's work = 6/60 = 1/10
10 children's 1 day's work = 1/12
1 children's 1 day's work = 1/120
4 children's 1 day's work = 4/120 = 1/30
∴ (6 women + 4 children) 1 day's work = 1/10 + 1/30 = 4/30
∴ They finish the work in 30/4 days = 7½ days
Q17. 5 men can complete a work in 10 days and the same work 6 women can complete in 15 days. How many days will 2 men and 3 women together take to complete the work ?
(a) 12(3/11) days
(b) 13(7/11) days
(c) 15(3/7) days
(d) 16(5/11) days
Answer: (b) 13(7/11) days
| 5 men's 1 day's work = | 1 |
| 10 |
| 1 men's 1 day's work = | 1 |
| 5 X 10 |
| 2 men's 1 day's work = | 2 | = | 1 |
| 50 | 25 |
| 6 women's 1 day's work = | 1 |
| 15 |
| 1 women's 1 day's work = | 1 |
| 6 X 15 |
| 3 women's 1 day's work = | 3 | = | 1 |
| 6 X 15 | 30 |
| Now (2 Men + 3 Women)'s 1 day's work = | 1 | + | 1 | = | 6 + 5 | = | 11 |
| 25 | 30 | 150 | 150 |
∴ Required day's = 150/11 = 13(7/11) days
Q18. Ram can do a work in 15 days. Rahim is 50% more efficient than Ram. The number of days, Rahim will take to do the same piece of work is
(a) 7 days
(b) 8 days
(c) 10 days
(d) 13 days
Answer: (c) 10 days
Ram's 1 day's work = 1/15
Rahim's 1 day's work = 150% of 1/15
| = | 150 | X | 1 |
| 100 | 15 |
= 1/10
Rahim can finish the work in 10 days.
Q19. Hari can do a work in 28 days. Jadu is 40% more efficient than Hari. The number of days, Jadu will take to do the same piece of work is
(a) 8 days
(b) 10 days
(c) 15 days
(d) 20 days
Answer: (d) 20 days
Hari's 1 day's work = 1/28
Jadu's 1 day's work = 140% of 1/28
| = | 140 | X | 1 |
| 100 | 28 |
= 1/20
∴ Jadu can finish the work in 20 days.
Q20. A works twice fast as B. If both of them can together finish a piece of work in 15 days then B alone can do it in
(a) 28 days
(b) 33 days
(c) 37 days
(d) 45 days
Answer: (d) 45 days
Let, B's one day's work = x
∴ A's one day's work = 2x
(A + B)'s 1 day's work = x + 2x = 3x
A/Q 3x = 1/15
⇒ x = 1/(15 X 3) = 1/45
∴ B's one day's work = 1/45
∴ B alone can do it in 45 days
Practice Test Exam